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shun"><meta itemprop="description" content="天官赐福，百无禁忌, 世中逢尔，雨中逢花"></span><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="航 順"></span><div class="body md" itemprop="articleBody"><p><img data-src="https://shun309.oss-cn-hangzhou.aliyuncs.com/photos/20230420135553.png" alt="" width="80%"></p><p>协同过滤算法捕获潜在的消费模式，包括特定于特定人口统计或用户的受保护信息的消费模式，例如：例如，性别种族和地点。这些编码的偏向可以影响推荐系统（RS）对进一步分离提供给各种人口统计子群的内容的决策，并且引起关于用户的受保护属性的公开的隐私问题。在这项工作中，本文研究了在保持推荐算法有效性的同时，将用户的特定保护信息从学习的交互表征中移除的可能性和挑战。具体来说，本文将对抗训练纳入到变分自编码器 MultVAE 架构中，从而形成了一个新的模型 —— 基于对抗训练的多项式自编码器模型（Adv-MultVAE），其目的是去除受保护属性的隐性信息，同时保持推荐性能。通过在两个数据集上进行实验来评估偏见缓解方法的有效性。结果表明，Adv-MultVAE 虽然在性能上略有下降（在 NDCG 和召回率方面），但在很大程度上缓解了模型的内在偏差。</p><blockquote><p>MultVAE：用于协同过滤的变分自编码器</p></blockquote><h1 id="介绍"><a class="anchor" href="#介绍">#</a> 介绍</h1><p>在推荐系统中，协同过滤算法主要基于收集到的用户 - 项目交互信息，例如：听音乐或看电影。在这些算法中，MultVAE 通过<strong>解码</strong>用户交互向量的<strong>变分自编码</strong>来学习推荐项目，并且在各种深度神经网络方法中显示出了最佳结果。虽然交互数据没有显式地包含有关受保护用户属性（如性别、种族或年龄）的信息，但模型仍然可以在其潜在嵌入中<strong>编码敏感信息</strong>。这在图 1a 中有所表现，例如在训练的 MultVAE 模型中关于男性和女性用户的点根据用户的性别形成相当分离的用户<strong>聚类</strong>。模型中的这些编码偏见可能导致<strong>基于用户人口统计学的 &quot;过滤气泡&quot; 增强</strong>，并加剧数据中现有的<strong>社会偏见</strong>，从而增加 RS 的不公平性。他们还可能提出关于建议或模型参数中敏感信息披露的隐私问题。</p><p><img data-src="https://shun309.oss-cn-hangzhou.aliyuncs.com/photos/20230117114929.png" alt="" width="67%"></p><p><strong>图 1</strong>. 攻击者网络的输出，旨在根据<em> LFM-2bDemoBias</em> 数据集上训练的 MultVAE 和 Adv-MultVAE 模型的潜在嵌入推断用户性别。蓝色和橙子标记分别对应于男性和女性用户。</p><p>针对这一问题，本文提出了一种新的偏差感知推荐模型 Adv-MultVAE，通过<strong>对抗式训练</strong>增强 MultVAE 以<strong>减少编码偏差</strong>。Adv-MultVAE 模型在学习提供有效推荐的同时，强制其潜在嵌入相对于消费者的给定<strong>受保护属性是不变的</strong>。这样的结果是降低了模型中子群体的可区分性（如图 1b 所示），因此在保持模型推荐性能的同时，使推荐对受保护属性 “盲”。本文特别采用了 MultVAE，因为它在各种不同的基于深度神经网络的方法中取得了最佳结果。</p><p>为了评估本文的方法在偏见缓解和推荐性能方面的优点，本文分别在电影和音乐领域的<em> MovieLens-1m</em> 和<em> LFM-2b-DemoBias</em> 数据集上进行了一组实验。本文将性别作为受保护属性，并评估攻击者网络的准确性和平衡准确性，以量化偏差缓解的效果。此外，本文还通过 NDCG 和召回率评估了模型的推荐性能。Adv-MultVAE 成功降低了固有性别偏见，同时略微降低了性能，主要是由于模型选择期间施加的挑战所致。</p><h1 id="对抗式变分自编码器"><a class="anchor" href="#对抗式变分自编码器">#</a> 对抗式变分自编码器</h1><p>在本节中，本文将介绍<strong>采用多项式似然法的对抗式变分自编码器（Adv-MultVAE）模型</strong>的架构。本文首先概述了基线 MultVAE，然后解释了本文的对抗性扩展。最后，本文描述了对抗性攻击的过程，用来评估偏见消除的有效性。图 2 描述了拟定 Adv-MultVAE 模型的概要。</p><p><img data-src="https://shun309.oss-cn-hangzhou.aliyuncs.com/photos/20230420120041.png" alt="" width="80%"></p><p><strong>图 2</strong>. Adv-MultVAE 概述。粗体箭头显示反向传递期间的梯度流，其中红色表示用于学习 <ins>与受保护属性 (𝒚) 不变的潜在嵌入 (𝒛)</ins> 的反向梯度。</p><h2 id="multvae"><a class="anchor" href="#multvae">#</a> MultVAE</h2><p>MultVAE 模型由两部分组成：</p><ul><li><p>第一部分是编码器网络<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑓</mi><mo stretchy="false">(</mo><mo separator="true">⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">𝑓(·)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord mathnormal" style="margin-right:.10764em">f</span><span class="mopen">(</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mclose">)</span></span></span></span>，输入为包含用户交互数据的𝒙，并推断低维潜在分布。使用<strong>标准高斯分布</strong>作为先验（N（0，𝐼））并使用<strong>重参数化技巧</strong>，该分布的特征在于𝝁和𝝈是可学习向量，从这些向量中采样潜在向量𝒛。</p></li><li><p>第二部分是解码器网络<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑔</mi><mo stretchy="false">(</mo><mo separator="true">⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">𝑔(·)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="mopen">(</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mclose">)</span></span></span></span>，其目的是通过预测𝒙′，从隐向量𝒛重构原始输入𝒙。本文参考 MultVAE 的损失函数为<em> Lrec (𝒙)</em>，定义如下：</p></li></ul><p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mrow><msup><mi mathvariant="script">L</mi><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi mathvariant="script">L</mi><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">U</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">T</mi></mrow></msup><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">(</mo><mi mathvariant="bold-italic">z</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mi mathvariant="bold-italic">x</mi><mo stretchy="false">)</mo><mo>−</mo><mi>β</mi><msup><mi mathvariant="script">L</mi><mrow><mi mathvariant="normal">K</mi><mi mathvariant="normal">L</mi></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="script">N</mi><mo stretchy="false">(</mo><mi mathvariant="bold-italic">μ</mi><mo separator="true">,</mo><mi mathvariant="bold-italic">σ</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mi mathvariant="script">N</mi><mo stretchy="false">(</mo><mn>0</mn><mo separator="true">,</mo><mi>I</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(1)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">\mathcal{L}^{\mathrm{rec}}(\boldsymbol{x})=\mathcal{L}^{\mathrm{MULT}}(g(\boldsymbol{z}),\boldsymbol{x})-\beta\mathcal{L}^{\mathrm{KL}}(\mathcal{N}(\boldsymbol{\mu},\boldsymbol{\sigma}),\mathcal{N}(0,I))\tag1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.7143919999999999em"><span style="top:-3.113em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathrm mtight">r</span><span class="mord mathrm mtight">e</span><span class="mord mathrm mtight">c</span></span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord"><span class="mord boldsymbol">x</span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span></span><span class="base"><span class="strut" style="height:1.1413309999999999em;vertical-align:-.25em"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.8913309999999999em"><span style="top:-3.113em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathrm mtight">M</span><span class="mord mathrm mtight">U</span><span class="mord mathrm mtight">L</span><span class="mord mathrm mtight">T</span></span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="mopen">(</span><span class="mord"><span class="mord"><span class="mord boldsymbol" style="margin-right:.04213em">z</span></span></span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord"><span class="mord boldsymbol">x</span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.1413309999999999em;vertical-align:-.25em"></span><span class="mord mathnormal" style="margin-right:.05278em">β</span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.8913309999999999em"><span style="top:-3.113em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathrm mtight">K</span><span class="mord mathrm mtight">L</span></span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathcal" style="margin-right:.14736em">N</span></span><span class="mopen">(</span><span class="mord"><span class="mord"><span class="mord boldsymbol">μ</span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord"><span class="mord boldsymbol" style="margin-right:.03704em">σ</span></span></span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord mathcal" style="margin-right:.14736em">N</span></span><span class="mopen">(</span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord mathnormal" style="margin-right:.07847em">I</span><span class="mclose">)</span><span class="mclose">)</span></span><span class="tag"><span class="strut" style="height:1.1413309999999999em;vertical-align:-.25em"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">1</span></span><span class="mord">)</span></span></span></span></span></span></p><p>其中<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="script">L</mi><mrow><mi>M</mi><mi>U</mi><mi>L</mi><mi>T</mi></mrow></msup></mrow><annotation encoding="application/x-tex">\mathcal{L}^{MULT}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.8413309999999999em;vertical-align:0"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.8413309999999999em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:.10903em">M</span><span class="mord mathnormal mtight" style="margin-right:.10903em">U</span><span class="mord mathnormal mtight">L</span><span class="mord mathnormal mtight" style="margin-right:.13889em">T</span></span></span></span></span></span></span></span></span></span></span></span> 是输入重构损失，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="script">L</mi><mrow><mi>K</mi><mi>L</mi></mrow></msup></mrow><annotation encoding="application/x-tex">\mathcal{L}^{KL}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.8413309999999999em;vertical-align:0"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.8413309999999999em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:.07153em">K</span><span class="mord mathnormal mtight">L</span></span></span></span></span></span></span></span></span></span></span></span> 是正则化损失，其目的是保持编码器的潜在分布接近于先验分布，其影响由超参数调整𝛽。更多详细信息请参考 Liang 等人。</p><blockquote><p>简而言之，<strong>重参数化技巧</strong>允许通过使用辅助随机变量重新参数化采样过程，来对随机变量𝒛进行采样，从而保持对𝝁和𝝈进行反向传播的能力。</p></blockquote><h2 id="adv-multvae"><a class="anchor" href="#adv-multvae">#</a> Adv-MultVAE</h2><p>本文提出的模型扩展了 MultVAE，引入了一个对抗网络，称为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi><mo stretchy="false">(</mo><mo separator="true">⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">h(·)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mclose">)</span></span></span></span>。对抗网络作为一个额外的头部被添加到潜在向量上，目的是从潜在向量预测𝒛用户的特定保护属性。<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi><mo stretchy="false">(</mo><mo separator="true">⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">h(·)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mclose">)</span></span></span></span> 是一个典型的前馈网络，它相对于包含用户的保护属性作为分类标签的𝒚向量进行优化。Adv-MultVAE 的训练过程旨在移除𝒛中受保护属性信息的同时，保持推荐性能。为此，将模型的损失定义为以下最小值 - 最大值问题：</p><p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable width="100%"><mtr><mtd width="50%"></mtd><mtd><mrow><mi><munder><mo><mo><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></mo></mo><mrow><mi>f</mi><mo separator="true">,</mo><mi>g</mi></mrow></munder></mi><msup><mi mathvariant="script">L</mi><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mo stretchy="false">)</mo><mo>−</mo><msup><mi mathvariant="script">L</mi><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">v</mi></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mo separator="true">,</mo><mi mathvariant="bold-italic">y</mi><mo stretchy="false">)</mo></mrow></mtd><mtd width="50%"></mtd><mtd><mtext>(2)</mtext></mtd></mtr></mtable><annotation encoding="application/x-tex">\underset{f,g}{\mathop{\mathrm{argminargmax}}}\mathcal{L}^{\mathrm{rec}}(\boldsymbol{x})-\mathcal{L}^{\mathrm{adv}}(\boldsymbol{x},\boldsymbol{y})\tag2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.8326559999999998em;vertical-align:-1.0826559999999998em"></span><span class="mord"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.6678600000000001em"><span style="top:-2.153452em;margin-left:0"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:.10764em">f</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:.03588em">g</span></span></span></span><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span><span class="mop"><span class="mop"><span class="mord"><span class="mord mathrm">a</span><span class="mord mathrm">r</span><span class="mord mathrm" style="margin-right:.01389em">g</span><span class="mord mathrm">m</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span><span class="mord mathrm">a</span><span class="mord mathrm">r</span><span class="mord mathrm" style="margin-right:.01389em">g</span><span class="mord mathrm">m</span><span class="mord mathrm">a</span><span class="mord mathrm">x</span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.0826559999999998em"><span></span></span></span></span></span></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.7143919999999999em"><span style="top:-3.113em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathrm mtight">r</span><span class="mord mathrm mtight">e</span><span class="mord mathrm mtight">c</span></span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord"><span class="mord boldsymbol">x</span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:.2222222222222222em"></span></span><span class="base"><span class="strut" style="height:1.149108em;vertical-align:-.25em"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.8991079999999999em"><span style="top:-3.113em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathrm mtight">a</span><span class="mord mathrm mtight">d</span><span class="mord mathrm mtight" style="margin-right:.01389em">v</span></span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord"><span class="mord boldsymbol">x</span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord"><span class="mord boldsymbol" style="margin-right:.03704em">y</span></span></span><span class="mclose">)</span></span><span class="tag"><span class="strut" style="height:1.9817639999999996em;vertical-align:-1.0826559999999998em"></span><span class="mord text"><span class="mord">(</span><span class="mord"><span class="mord">2</span></span><span class="mord">)</span></span></span></span></span></span></p><p>其中对抗网络的损失<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="script">L</mi><mrow><mi>a</mi><mi>d</mi><mi>v</mi></mrow></msup></mrow><annotation encoding="application/x-tex">\mathcal{L}^{adv}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.849108em;vertical-align:0"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.849108em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">d</span><span class="mord mathnormal mtight" style="margin-right:.03588em">v</span></span></span></span></span></span></span></span></span></span></span></span> 被定义为受保护属性的预测值和实际值之间的交叉熵损失（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="script">L</mi><mrow><mi>C</mi><mi>E</mi></mrow></msup></mrow><annotation encoding="application/x-tex">\mathcal{L}^{CE}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.8413309999999999em;vertical-align:0"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.8413309999999999em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:.07153em">C</span><span class="mord mathnormal mtight" style="margin-right:.05764em">E</span></span></span></span></span></span></span></span></span></span></span></span>）：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="script">L</mi><mrow><mi>a</mi><mi>d</mi><mi>v</mi></mrow></msup></mrow><annotation encoding="application/x-tex">\mathcal{L}^{adv}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.849108em;vertical-align:0"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.849108em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">d</span><span class="mord mathnormal mtight" style="margin-right:.03588em">v</span></span></span></span></span></span></span></span></span></span></span></span>（𝒙，𝒚）= <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="script">L</mi><mrow><mi>C</mi><mi>E</mi></mrow></msup></mrow><annotation encoding="application/x-tex">\mathcal{L}^{CE}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:.8413309999999999em;vertical-align:0"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.8413309999999999em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:.07153em">C</span><span class="mord mathnormal mtight" style="margin-right:.05764em">E</span></span></span></span></span></span></span></span></span></span></span></span>（（𝒛），𝒚）。事实上，公式中定义的损失函数 2 的目标是在给定时最大化<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi><mo stretchy="false">(</mo><mo separator="true">⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">h(·)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mclose">)</span></span></span></span> 的预测能力以发现所有敏感信息𝒛，同时最小化𝒛与受保护属性相关的编码信息。</p><p>考虑到众所周知的优化 min - max 损失函数的复杂性，在前期工作的基础上，本文在𝒛和对抗网络<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi><mo stretchy="false">(</mo><mo separator="true">⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">h(·)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mclose">)</span></span></span></span> 之间增加了一个<strong>梯度反转层</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑔</mi><mi>𝑟</mi><mi>𝑙</mi><mo stretchy="false">(</mo><mo separator="true">⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">𝑔𝑟𝑙(·)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="mord mathnormal" style="margin-right:.02778em">r</span><span class="mord mathnormal" style="margin-right:.01968em">l</span><span class="mopen">(</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mclose">)</span></span></span></span>。在训练过程中，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑔</mi><mi>𝑟</mi><mi>𝑙</mi><mo stretchy="false">(</mo><mo separator="true">⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">𝑔𝑟𝑙(·)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="mord mathnormal" style="margin-right:.02778em">r</span><span class="mord mathnormal" style="margin-right:.01968em">l</span><span class="mopen">(</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mclose">)</span></span></span></span> <strong>在前向传播中作为恒等函数，而在后向传播中它将计算出的梯度缩放−\lambda</strong>。<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑔</mi><mi>𝑟</mi><mi>𝑙</mi><mo stretchy="false">(</mo><mo separator="true">⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">𝑔𝑟𝑙(·)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="mord mathnormal" style="margin-right:.02778em">r</span><span class="mord mathnormal" style="margin-right:.01968em">l</span><span class="mopen">(</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mclose">)</span></span></span></span> 网络在推断时对模型没有任何影响。<strong>本文将参数 \lambda 称为梯度反转缩放</strong>。通过在模型中使用<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>𝑔</mi><mi>𝑟</mi><mi>𝑙</mi><mo stretchy="false">(</mo><mo separator="true">⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">𝑔𝑟𝑙(·)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="mord mathnormal" style="margin-right:.02778em">r</span><span class="mord mathnormal" style="margin-right:.01968em">l</span><span class="mopen">(</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mclose">)</span></span></span></span>，使得方程中的整体损失最小。公式 2 中的总体损失函数现在可以重新表述为标准的风险最小化设定：（本段内容：增加梯度反转层，是损失函数（2）变换成了损失函数（3））</p><p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.15999999999999992em" columnalign="center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi><munder><mo><mi>arg</mi><mo>⁡</mo><mi>min</mi><mo>⁡</mo><mi mathvariant="script">L</mi></mo><mrow><mi>f</mi><mo separator="true">,</mo><mi>g</mi><mo separator="true">,</mo><mi>h</mi></mrow></munder></mi><mo>=</mo><msup><mi mathvariant="script">L</mi><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mi mathvariant="script">L</mi><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">v</mi></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mo separator="true">,</mo><mi mathvariant="bold-italic">y</mi><mo stretchy="false">)</mo><mo separator="true">,</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><msup><mi mathvariant="script">L</mi><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">v</mi></mrow></msup><mo stretchy="false">(</mo><mi mathvariant="bold-italic">x</mi><mo separator="true">,</mo><mi mathvariant="bold-italic">y</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi mathvariant="script">L</mi><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">E</mi></mrow></msup><mo stretchy="false">(</mo><mi>h</mi><mo stretchy="false">(</mo><mi>g</mi><mi>i</mi><mi>r</mi><mi>l</mi><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mi mathvariant="bold-italic">y</mi><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{array}{c}\underset{f,g,h}{\arg\min\mathcal{L}}=\mathcal{L}^{\mathrm{rec}}(\boldsymbol{x})+\mathcal{L}^{\mathrm{adv}}(\boldsymbol{x},\boldsymbol{y}),\\ \mathcal{L}^{\mathrm{adv}}(\boldsymbol{x},\boldsymbol{y})=\mathcal{L}^{\mathrm{CE}}(h(girl(z),\boldsymbol{y})\end{array}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.140872em;vertical-align:-1.3204360000000002em"></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:.5em"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8204359999999997em"><span style="top:-3.9713279999999997em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:.68333em"><span style="top:-2.153452em;margin-left:0"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:.10764em">f</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:.03588em">g</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">h</span></span></span></span><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span><span class="mop"><span class="mop">ar<span style="margin-right:.01389em">g</span></span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mop">min</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord mathcal">L</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.0826559999999998em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.664392em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathrm mtight">r</span><span class="mord mathrm mtight">e</span><span class="mord mathrm mtight">c</span></span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord"><span class="mord boldsymbol">x</span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:.2222222222222222em"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.849108em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathrm mtight">a</span><span class="mord mathrm mtight">d</span><span class="mord mathrm mtight" style="margin-right:.01389em">v</span></span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord"><span class="mord boldsymbol">x</span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord"><span class="mord boldsymbol" style="margin-right:.03704em">y</span></span></span><span class="mclose">)</span><span class="mpunct">,</span></span></span><span style="top:-2.039564em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.849108em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathrm mtight">a</span><span class="mord mathrm mtight">d</span><span class="mord mathrm mtight" style="margin-right:.01389em">v</span></span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord"><span class="mord boldsymbol">x</span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord"><span class="mord boldsymbol" style="margin-right:.03704em">y</span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:.2777777777777778em"></span><span class="mord"><span class="mord"><span class="mord mathcal">L</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.8413309999999999em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathrm mtight">C</span><span class="mord mathrm mtight">E</span></span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:.03588em">g</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:.02778em">r</span><span class="mord mathnormal" style="margin-right:.01968em">l</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:.04398em">z</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mord"><span class="mord"><span class="mord boldsymbol" style="margin-right:.03704em">y</span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.3204360000000002em"><span></span></span></span></span></span><span class="arraycolsep" style="width:.5em"></span></span></span></span></span></span></span></p><p>该公式使得能够通过标准的基于梯度的损失最小化来优化模型。</p><h2 id="adversarial-attacks"><a class="anchor" href="#adversarial-attacks">#</a> Adversarial Attacks</h2><p>在对模型 (无论是 MultVAE 还是 Adv-MultVAE) 进行训练后，本文考察被保护属性的信息在多大程度上保留在模型中，即这种信息在多大程度上仍能被恢复。为此，一旦训练完成，将攻击者网络<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>h</mi><mrow><mi>a</mi><mi>t</mi><mi>k</mi></mrow></msup><mo stretchy="false">(</mo><mo separator="true">⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">ℎ^{atk} ( · )</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.099108em;vertical-align:-.25em"></span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.849108em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight" style="margin-right:.03148em">k</span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mclose">)</span></span></span></span> 引入到模型中，该模型旨在从隐向量𝒛预测受保护属性𝒚。与<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi><mo stretchy="false">(</mo><mo separator="true">⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">ℎ( · )</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-.25em"></span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mclose">)</span></span></span></span> 类似，将攻击者<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>h</mi><mrow><mi>a</mi><mi>t</mi><mi>k</mi></mrow></msup><mo stretchy="false">(</mo><mo separator="true">⋅</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">ℎ^{atk} ( · )</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.099108em;vertical-align:-.25em"></span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:.849108em"><span style="top:-3.063em;margin-right:.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight" style="margin-right:.03148em">k</span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mpunct">⋅</span><span class="mspace" style="margin-right:.16666666666666666em"></span><span class="mclose">)</span></span></span></span> 定义为前馈网络。在训练攻击者的过程中，所有模型参数保持不变 (冻结)，仅更新攻击者参数。攻击者的预测性能 - - 相对于随机预测者 - - 被用作度量来量化底层模型中的偏差程度。</p><p>paper：<span class="exturl" data-url="aHR0cHM6Ly9kbC5hY20ub3JnL2RvaS9hYnMvMTAuMTE0NS8zNDc3NDk1LjM1MzE4MjA=">https://dl.acm.org/doi/abs/10.1145/3477495.3531820</span></p><p>codes：<span class="exturl" data-url="aHR0cHM6Ly9naXRodWIuY29tL0NQSktVL2Fkdi1tdWx0dmFl">https://github.com/CPJKU/adv-multvae</span></p><div class="tags"><a href="/tags/%E6%8E%A8%E8%8D%90%E7%B3%BB%E7%BB%9F/" rel="tag"><i class="ic i-tag"></i> 推荐系统</a> <a href="/tags/%E6%96%B0%E9%97%BB%E6%8E%A8%E8%8D%90/" rel="tag"><i class="ic i-tag"></i> 新闻推荐</a> <a 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class="toc-item toc-level-2"><a class="toc-link" href="#multvae"><span class="toc-number">2.1.</span> <span class="toc-text">MultVAE</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#adv-multvae"><span class="toc-number">2.2.</span> <span class="toc-text">Adv-MultVAE</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#adversarial-attacks"><span class="toc-number">2.3.</span> <span class="toc-text">Adversarial Attacks</span></a></li></ol></li></ol></div><div class="related panel pjax" data-title="系列文章"><ul><li class="active"><a href="/posts/b2c2f458/" rel="bookmark" title="Adv-MultVAE：基于对抗学习的隐私保护推荐算法">Adv-MultVAE：基于对抗学习的隐私保护推荐算法</a></li><li><a href="/posts/f8ce3000/" rel="bookmark" title="Hetedp：基于异构图神经网络的隐私保护推荐">Hetedp：基于异构图神经网络的隐私保护推荐</a></li><li><a href="/posts/cc988ffe/" rel="bookmark" title="UA-FedRec：对联邦新闻推荐的无目标攻击">UA-FedRec：对联邦新闻推荐的无目标攻击</a></li><li><a href="/posts/ef078385/" rel="bookmark" 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